Two resistances of \( 100\,\Omega \) and \( 200\,\Omega \) are connected in series across a 20 V battery as shown in figure below. The reading in a \( 200\,\Omega \) voltmeter connected across the \( 200\,\Omega \) resistance is ___________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10 V
A real voltmeter has a finite resistance, so when it is connected across a resistor it is in parallel with that resistor and lowers the resistance of that part of the circuit.
\( \displaystyle R_{p} = \frac{200 \times 200}{200 + 200} = 100\,\Omega \)
This combination is in series with the \( 100\,\Omega \) resistor.
\( R_{\mathrm{total}} = 100 + 100 = 200\,\Omega \)
\( I = 20\,\mathrm{V} / 200\,\Omega = 0.1\,\mathrm{A} \)
The voltmeter reads the potential difference across the parallel part.
\( V = I R_{p} = 0.1\,\mathrm{A} \times 100\,\Omega = 10\,\mathrm{V} \)